# Frampton & Hung's Higgs mass ansatz

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1. Oct 16, 2013

### mitchell porter

http://arxiv.org/abs/1310.3904
A Possible Reason for MH ≃ 126 GeV
Paul H. Frampton, Pham Q. Hung
(Submitted on 15 Oct 2013)
It is speculated that a possible reason for the scalar mass MH ≃ 126 GeV is equality of the lifetimes for vacuum decay and instanton-induced proton decay.

2. Oct 16, 2013

### MathematicalPhysicist

Isn't Paul Frampton the Prof who got caught with smuggling drugs in south america for a beloved model?

How can a smart man fall for such a scam?

3. Oct 16, 2013

### mitchell porter

That has nothing to do with this thread, please discuss it elsewhere.

4. Oct 17, 2013

### lpetrich

My first thought is: is there any theoretical reason why those decay lifetimes ought to be equal? Higgs vacuum instability and proton decay by instantons are two different mechanisms, so I don't see how they would be connected, let alone give the same lifetime. I read Frampton and Hung's paper, and they don't give any hint either.

Those two effects are both quantum tunneling effects, but as far as I can tell, that's most of what they have in common. A well-known bit of quantum tunneling is alpha decay of heavy nuclei, and alpha-decay lifetimes vary like crazy. So even closely-related tunneling effects can have drastically differing rates.

5. Oct 23, 2013

### mitchell porter

Another reason you wouldn't expect them to be related, is that the rate of proton decay depends on the rate at which a particular event occurs inside a proton, whereas the rate of vacuum decay depends on the rate at which a particular event occurs inside a cosmological horizon.

But perhaps that would be the point - a hypothetical BSM theory in which the Frampton-Hung relation was not just coincidence, would explain the ratio "horizon radius / proton radius".

6. Oct 23, 2013

### MathematicalPhysicist

Does this article depend on something like proton decay which as far as I can tell haven't yet been verified even?

7. Oct 23, 2013

### mitchell porter

The type of proton decay that people have unsuccessfully looked for, is based on grand unified theories in which there are new ultraheavy bosons that can directly convert a quark to a lepton. But there is another type of proton decay which is already implied by the standard model, but which is unobservably rare at the current temperature of the universe (though it may have had significant effects in the early universe).

They are talking about this other type of proton decay, that takes about a googol years to happen. It's weird, it combines an "axial anomaly" in which the overall sum of lefthanded and righthanded fermions isn't conserved, with an ultra-rare "sphaleron" configuration of the electroweak gauge fields. Somehow the consequence is that a proton goes in and antileptons come out! I want to understand it.

8. Oct 24, 2013

### MathematicalPhysicist

The question is "Is it empirically testable?"

If not then it's not any different than believing in a personal God.

9. Oct 25, 2013

### MathematicalPhysicist

BTW, is there a model or a theory that posits that protons never decay?

10. Oct 27, 2013

### lpetrich

The only proposed GUT that I know of that does not predict proton decay is trinification. It has gauge group SU(3)*SU(3)*SU(3), with one of the SU(3)'s becoming the QCD SU(3). The other two SU(3)'s become the electroweak SU(2)*U(1).

All the others do, because they have elementary-fermion multiplets that include quarks and leptons. That's what leads to baryon-number violation, and from that, protons decaying.

Every hadron can decay in proton-decay fashion, but nearly all of them decay much faster by Standard-Model interactions. However, neutrons can be stabilized against SM-interaction decay by being bound in nuclei. So proton-decay experiments also measure the decay rate of bound neutrons in otherwise-stable nuclei.

11. Oct 28, 2013

### Myslius

12. Oct 28, 2013

### torus

How is this supposed to work? I thought Instantons (and sphalerons) change baryon and lepton number only in steps of 3 (the number of generations). Therefore the proton can not decay via instantons...

Even in 't Hooft's cited paper Phys. Rev. Lett. 37, 8-11 (1976) proton decay is not considered, but rather the annihilation of proton and neutron to two leptons (he uses only two generations).

13. Oct 28, 2013

### fzero

Yes, if you just have a bare proton then energy conservation would seem to prevent it from decaying due to EW instantons. However, the 't Hooft process would cause the instability of all $A>1$ nuclei, which has many of the same consequences of proton decay.

14. Nov 1, 2013

### mitchell porter

It would be much too rare for anyone to see it happen. However, this sphaleron-induced decay is a process implied by the standard model and by our understanding of nonperturbative quantum field theory. It is not an extra postulate - I didn't make that clear.

It might be possible to indirectly test for the reality of electroweak sphalerons in cosmological data, since the sphalerons should be much more common in the high temperatures of the early universe. Actually, the challenge for the standard model here is that sphalerons might have been useful to produce the universe's baryon asymmetry (excess of matter over antimatter), except that even at those temperatures, they are still not common enough to produce the magnitude of matter excess that we see. So the standard-model sphalerons would have to be just part of a bigger, beyond-standard-model picture of all the processes occurring after the big bang.

This question gets even better when you ask it about the whole Frampton-Hung scenario. :-)

They are interested in the idea that the Higgs field is currently in a metastable state, and that it will eventually quantum-tunnel its way to the true ground state, in which the Higgs energy density becomes GUT-scale, all particles become supermassive, and atoms and nuclei as we know them would cease to exist. Their idea is that if the timescale of this vacuum decay is similar to the timescale of sphaleron-induced proton decay, that implies a Higgs boson mass that is about what we see.

This hypothesis is just a new variation on the now familiar observation that the observed Higgs boson mass is right on the edge between metastability and absolute stability of the Higgs vacuum. If we were to make the alternative hypothesis that the Higgs mass is the minimum mass for which the Higgs vacuum is absolutely stable - lasts forever - then that also lands us near the observed mass. Or if we were to suppose that the Higgs vacuum's lifetime is just on the order of ten billion years (this could be an anthropic argument), once again, that will land us near the observed mass.

My point is that there's nothing clearly special about this googol-year timescale derived from thinking about sphalerons. Any timescale from tens of billions of years, to forever, would imply a critical value of Higgs mass (well, in the case of "forever", you have to assume that it's the minimum mass that produces absolute stability, in order to get near the critical value). I should also qualify this statement - there are considerable theoretical uncertainties about exactly which values of Higgs mass and top mass, lie on which side of the boundary between metastability and absolute stability. There are competing claims which use different approximations. But they're all in the same ballpark, and the fact that it matters e.g. whether you calculate to two loops or to three loops, at least demonstrates that we are close to criticality in some sense.

So the significance of this paper by Frampton & Hung is that they are suggesting a specific new line of inquiry, regarding what could be the reason for criticality or near-criticality of the Higgs. The question is whether this new direction makes much sense, or could be made to make sense.

In that regard, the first thing to observe is that part of their scenario is that dark energy has disappeared by the time the Higgs vacuum decay occurs. I think that what is being talked about here is not just the occurrence of Higgs vacuum decay somewhere in the universe, but the domination of the true ground state throughout the universe. Recall that these decays are supposed to happen in the far future. The bubble of true vacuum (true ground state) expands at the speed of light once it appears, but in a Lambda-CDM cosmology of accelerating expansion, the universe itself is also expanding very rapidly by the time we are a googol years or more in the future; whereas, if the dark energy has disappeared, so will the acceleration, and the bubble of true vacuum can expand to reach the cosmological horizon a little more quickly.

I am assuming - I ought to check Frampton & Hung's reference 27, but for the sake of moving the discussion along, I'll just assume, and check later - that this is the reason why the lifetime of the metastable Higgs vacuum is a little longer, in the cosmology where dark energy persists.

In their paper Frampton and Hung go a little further and speculate - reasonably enough, given the connection that they wish to make - that the dark energy actually disappears when the vacuum decay occurs. This is where we can actually start to think about mechanisms. My first thought is of quintessence. The simplest idea about dark energy is that it's just vacuum energy, but the next simplest is that vacuum energy is zero and that dark energy is the energy in a new scalar field, usually called the quintessence field.

So perhaps the idea is that there's a single big scalar potential involving the Higgs scalar and the quintessence scalar, and the true ground state is one where the Higgs field takes an enormous leap in energy density, while the quintessence field drops to zero.

But this still provides no mechanism for the desired connection with sphalerons. The rate of occurrence of sphalerons, according to F&H equation 4, depends mostly on the Weinberg angle and the electromagnetic coupling constant. The rate of decay of the combined Higgs-quintessence vacuum will depend on various coefficients in the combined scalar potential. I suppose this framework would at least get us to the stage of being able to reason about the idea more concretely. Given this framework (SM + coupled Higgs/quintessence vacuum decay), you could then try to make an anthropic argument, or look for a still-deeper theory in which all these parameters were correlated in the desired way.

The other thought I've had, is that maybe F&H are thinking that the proton decay causes the vacuum decay. More precisely, that the sphaleron which causes proton decay on googol-year timescales, also causes the Higgs vacuum decay and the disappearance of dark energy. If that were so, it would explain the coincidence of timescales.

But this is problematic for two reasons. First, the sphaleron is a theoretically well-studied phenomenon of the electroweak field. One would have to suppose some novel interplay with the scalar sector, for it to have such drastic effects.

Second, what about the sphalerons in the early universe? If an electroweak sphaleron can initiate Higgs vacuum decay, and if sphalerons were relatively abundant after the big bang, then we shouldn't even be here, the universe should already be dominated by the true vacuum, with all particles supermassive. I already mentioned that there's an intriguing failed connection between sphalerons and baryon asymmetry, maybe there's some conceptual reverse backflip which somehow solves that problem and this one at the same time, but I'm failing to see it.

So the idea isn't working so far, but it's quite stimulating because of what it brings together.